Scrum-half Perenara, 32, extended his all-time record for Super Rugby tries to 64 in a 31-27 defeat at the Auckland Blues last Saturday, a week after moving past his former Hurricanes team-mate Julian Savea.
"He's knocking on the All Blacks door and I would be surprised if they look past him," ex-England flanker Shields told AFP Thursday.
All Blacks coach Scott Robertson will name his squad next month for the two-Test home series with England in July.
Perenara was sidelined for more than a year and only returned to Super Rugby in March after twice needing surgery to repair his Achilles, which snapped while playing against England in November 2022.
"It speaks volumes for his mindset with the way he trains, after back-to-back Achilles injuries," said Shields.
"Most people would be close to calling it quits.
"He has put in a lot of hard work and it's why he is back playing at this level and is the top try scorer."
Shields said the Hurricanes must learn from defeat at the Blues as they prepare to host strugglers Moana Pasifika on Friday.
The Auckland loss was only the Hurricanes' second this season and it dropped them to second in the table for the first time.
"It's a tough pill to swallow. We're a bit disappointed as we didn't give it our best effort," Shields said.
"We needed to take a couple more opportunities and there were a couple of tactical aspects we could have changed."
Victory will put the Hurricanes back on top before the Blues host the Otago Highlanders on Saturday.
With three games left, the Blues and Hurricanes are locked in the battle for top spot, which will determine home advantage when the play-offs start in June.
Auckland-based Moana have won three of their 11 games this season, pushing the Waikato Chiefs early last Friday before succumbing to a 43-7 defeat.
"They aren't afraid to chance their arm, if you give them a good head of steam they are a pretty hard team to stop," Shields said.
"You saw that against the Chiefs, with their big ball carriers they're dangerous, so we've got to be more physical."
